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Mathematical Problems in Engineering
Volume 2015, Article ID 640107, 3 pages
Research Article

Phase Synchronization Is the Amplified Result by the Hilbert Transform

1Department of Physics, National Kaohsiung Normal University, Kaohsiung 824, Taiwan
2Graduate Institute of Science Education & Environmental Education, National Kaohsiung Normal University, Kaohsiung 824, Taiwan

Received 30 September 2014; Accepted 26 December 2014

Academic Editor: Mo Li

Copyright © 2015 Ming-Chi Lu et al. This is an open access article distributed under the Creative Commons Attribution License, which permits unrestricted use, distribution, and reproduction in any medium, provided the original work is properly cited.


We investigate the interplay between phase synchronization and amplitude synchronization in nonlinear dynamical systems. It is numerically found that phase synchronization intends to be established earlier than amplitude synchronization. Nevertheless, amplitude synchronization (or the state with large correlation between the amplitudes) is crucial for the maintenance of a high correlation between two time series. A breakdown of high correlation in amplitudes will lead to a desynchronization of two time series. It is shown that these unique features are caused essentially by the Hilbert transform. This leads to a deep concern and criticism on the current usage of phase synchronization.